# Consumer Preferences - PDF

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```					Lecture 1 Consumer Preferences

2. The consumer choice problem

3. Consumer preferences

4. Utility Function

5. Consumer Constraints

Economics? - - - allocation of scarce resources Microeconomics? - - Allocation of scarce resources at “individual” level

• Consumer • Producer

2. Consumer choice problem

Individual decision problem 1. there is a set of mutually exclusive alternatives 2. one alternative must be chosen

1+2= ALLOCATION OF SCARCE RESOURCES

- ex: limited amount of money to be spent on different bundles of goods - ex: limited amount of time to be spent on different activities

QUESTION: How do individual choose a given alternative among all mutual exclusive alternative?

ANSWER: to answer this question we need to contruct a theory of consumer choice…

2 APPROACHES: a) “Axiomatic approach”: we impose some assumptions on the consumer preferences and we derive the consumer behaviour - we construct a theory that predicts a certain consumer behaviour. b) “Behavioral approach”: we start from the consumer behaviour and, imposing some consistency assumption, we try to construct a theory - - we observe the behaviour and we try to derive a theory that rationalize this behaviour

Q: are a) and b) consistent? - - - not always…

• Remember that the consumer choice problem is “choose an option among mutual exclusive alternatives”

• Hence we can expect that the consumer choice depends on two elements:

1. Tastes (preferences)

2. Feasible alternatives (contraints)

2 A: preferences

Consumer preferences: axiomatic approach

Consumer tastes

preferences relations

AXIOMS: RATIONALITY

Definition: a preference relation  is rational if it satisfies: i) ii) completeness transitivity

Other properties: Monotonicity

Local non-satiation (weak version of desirability)

Indifference curves Given the preference relation  and a consumption bundle x, we can define three related set of consumption bundles:

- indifference set (indifference curve - upper contour set - lower contour set

note: local non-satiation - - this rules out “thick indifference sets”

IMPORTANT ASSUMPTION: CONVEXITY

Definition: the preference relation  is convex if the upper countour set is convex

Convexity=diminuishing marginal rate of substitution

Utility function A utility function is a way to describe preferences Definition: U : X → ℜ is a utility function representing preferences if ∀x1 , x2 ∈ X ⇒ x1  x2 ⇔ U ( x1 ) ≥ U ( x2 )

UNIQUENESS Is the utility function unique? NO - - ANY MONOTONIC TRANSFORMATION REPRESENTS THE SAME PREFERENCES

UTILITY IS AN ORDINAL CONCEPT NOT A CARDINAL CONCEPT!

EXISTENCE Can preferences be always represented by a utility function? NO!

Proposition: a preference relation  can be represented by a utility function only if it is rational

Note: rationality is necessary for utility representation but is not sufficient!

For utility representation we also need CONTINUITY!

Definition: a preference relation  is continuous if it is preserved under limits: For any sequence of pairs ( x , y ) n=1 with x  y for all n, given
n n

{

n

n ∞

}

x = lim

n→∞

x and
n

y = lim

n →∞

y , then x  y .
n

Continuity: consumer preferences cannot have “jumps”, no reversal of preferences at the limits.

EXAMPLE OF NON-CONTINOUS PREFERENCES: LEXICOGRAFIC PREFERENCES

Theorem: suppose that the rational preference relation is  is continuous. Then there is a continuous utility function u(x) that represents this preference.

2B: Constraints Consumption choices are limited by two types of constraints:

- Physical constraints - Economic constraints

Physical constraint= consumption set Economic constraint= budget contraint

Definition: the competitive budget set

L B p , w = x ∈ ℜ + : px ≤ w

{

} is the set of

all feasible consumption bundles for the consumer facing market prices p and having income w.

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